You could try something like this:

use strict;
use warnings;

open (my $in,"<", "/tmp/logbook.log") or die "can not open datei: $!";
my @errors = grep /error/i, <$in>;
my $file = '/tmp/ok.txt';
open my $out, ">", $file or die "Kann Datei $file nicht zum Schreiben 
+oeffnen: $!\n";
if (@errors) {
   print $out @errors;
}
else {
   print $out "OK!\n";
}
close($in);
close($out);
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If the logbook.log file has something like this:

line1 has an error
line2 does not
ERROR on line 3

the following output is in the ok.txt file:

line1 has an error
ERROR on line 3